UBC-constrained non-probabilistic reliability-based optimization of structures with uncertain-but-bounded parameters

Luo, Zhenxian; Wang, Xiaojun; Shi, Qinghe; Li, Dongliang

doi:10.1007/s00158-020-02697-y

Cited by 9 publications

(3 citation statements)

References 42 publications

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“…Therefore, the traditional single-source uncertainty model optimization design methods, especially those derived from probability theory, may no longer be applicable. [24][25][26] To solve the problem, nonprobabilistic methods [27][28][29][30] are explored.…”

Section: Literature Reviewmentioning

confidence: 99%

Reliability analysis of mechanisms with mixed uncertainties using polynomial chaos expansion

Fang

Wang

Sha

et al. 2023

Quality & Reliability Eng

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In order to quantify the effect of mixed uncertainties on the reliability of mechanisms, this paper proposes a method for analyzing the reliability of mechanisms with mixed uncertainties using polynomial chaos expansion. Based on the performance margin theory, a mechanism reliability model considering mixed uncertainties is developed, and the Sobol indices can be easily calculated by an arbitrarily polynomial chaos expansion (aPCE) of the reliability function to quantify the independent contribution of each parameter to the global sensitivity and the effect of parameter coupling. Additionally, this paper also introduces a mixed uncertainties propagation method based on PCE, which treats cognitive uncertainties as fuzzy variables, converts the fuzzy variable into an interval variable using cut set theory, and transforms the PCE containing interval uncertainties into a Bernstein polynomial to calculate the membership function of the output quantity and the non-probabilistic reliability index by area method. The final case study of a simplified automaton motion mechanism illustrates that the proposed method is effective and convincing, and the mechanism reliability decreases with increasing mixed uncertainties. The mechanism reliability index considering mixed uncertainties will give a more conservative reliability estimation.

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Section: Literature Reviewmentioning

confidence: 99%

Reliability analysis of mechanisms with mixed uncertainties using polynomial chaos expansion

Fang

Wang

Sha

et al. 2023

Quality & Reliability Eng

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“…With the development of interval optimization theory, scholars further combined interval optimization with reliability analysis and applied them into engineering structural design. For instance, Luo et al [16] proposed the non-probabilistic reliability-based design optimization (NRBDO) method for structures with interval parameters, which utilized the ultimate bearing capacity to reflect structural reliability. Wang et al [17] presented a kind of NRBDO method based on interval model, which utilized the non-probabilistic reliability index to measure structural reliability.…”

Section: Introductionmentioning

confidence: 99%

Reliability-based Design Optimization of Structures with Disturbed Design Variables and Dependent Uncertainties

Guan

Wan

2022

J. Phys.: Conf. Ser.

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To ensure the safety of engineering structures under disturbed design variables and dependent uncertainties, a new reliability-based design optimization method was proposed in this paper. The optimization model was firstly established by adding the additional constraints that considers the disturbance of design variables. Then, the multidimensional parallelepiped model was used to describe the uncertainties and to further process their correlation. Further, the structural reliability was analyzed by interval analysis and reliability-based possibility degree of interval model. Finally, the solving algorithm was constructed. Such the algorithm was applied to a numerical example and the structural design of augmented reality glasses, among which the former demonstrated the effectiveness of proposed algorithm in dealing with disturbance of design variables and correlation between uncertainties, while the latter showed the applicability of the algorithm in engineering structural design.

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“…Unfortunately, the distribution information can be accurately known [27] in some cases. The lower and upper bounds of the uncertain parameters is easily obtained in practice, which can be well-quantified by the interval mathematics [28]. Therefore, the convex model, based on interval mathematics, can serve as a powerful supplement to this part [29].…”

Section: Introductionmentioning

confidence: 99%

Size-Dependent Mechanical Behaviors of Defective FGM Nanobeam Subjected to Random Loading

2022

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Considering the uncertainties of the materials and loads, the nanobeam made of functionally graded materials were investigated based on the non-local elastic theory. The spline finite point method (SFPM) was established to analyze the bending behavior of the nanobeam-based Timoshenko theory. In comparison with finite element method (FEM), SFPM has higher accuracy. Further, the multi-source uncertainties are considered, material properties are quantified as interval parameters, and loads are taken as random parameters. To deal with the problems with two types of uncertainties coexisting, a hybrid uncertain analysis model was established, and the method of polynomial chaos expansion and dimensional wise (PCE–DW) analysis was proposed to predict the response of nanobeam in the hybrid uncertain system. Numerical examples ultimately illustrate the effectiveness of the model and solution techniques, compared with MCS. The results furtherly verify the efficiency and accuracy.

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UBC-constrained non-probabilistic reliability-based optimization of structures with uncertain-but-bounded parameters

Cited by 9 publications

References 42 publications

Reliability analysis of mechanisms with mixed uncertainties using polynomial chaos expansion

Reliability analysis of mechanisms with mixed uncertainties using polynomial chaos expansion

Reliability-based Design Optimization of Structures with Disturbed Design Variables and Dependent Uncertainties

Size-Dependent Mechanical Behaviors of Defective FGM Nanobeam Subjected to Random Loading

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